In linear algebra, a matrix is orthogonal if each row is perpendicular to every other row. This can be brute force tested by taking the dot product of every pair distinct rows, and ensuring that the result is zero in each case. Some orthogonal matrices:

[from mathematics] Mutually independent;
well separated; sometimes, irrelevant to. Used in a generalization
of its mathematical meaning to describe sets of primitives or
capabilities that, like a vector basis in geometry, span the entire
`capability space' of the system and are in some sense
non-overlapping or mutually independent. For example, in
architectures such as the PDP-11 or VAX where all or nearly all
registers can be used interchangeably in any role with respect to
any instruction, the register set is said to be orthogonal. Or, in
logic, the set of operators `not' and `or' is orthogonal, but
the set `nand', `or', and `not' is not (because any one of
these can be expressed in terms of the others). Also used in
comments on human discourse: "This may be orthogonal to the
discussion, but...."

The Orthogonal series is a sci-fi trilogy by Greg Egan, composed of The Clockwork Rocket, The Eternal Flame, and The Arrows of Time. It is an example of how you can simultaneously be hard sci-fi and violate the laws of physics.

Let's talk about geometry. The Pythagorean theorem tells you a² + b² = c², relating two possible paths you can take through space. Taking a different path increases the distance you need to travel.

Note I said space. What about paths through time? Well, as it turns out, the Pythagorean theorem for time is a² - b² = c². That is, taking a "longer" path reduces time. If you've ever heard of how travelling near the speed of light causes your personal time to be shorter, this is the formalization of why.

What does this have to with a sci-fi novel? Simple.

What if Pythagorean theorem for time was a² + b² = c², just like space? Orthogonal is about such a universe.